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Proof step 8 from proof ocs-same-length-all (previous step)

∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a) ⊦ a0 ' + x0 = a ' + mklist(a, # x0) ↔ (∀ b. b = a0 ∨ b ∈ x0 → b = a)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ a ' + x = b ' + y ↔ a = b ∧ x = y
Proof step 10:
∀ a. x0 = mklist(a, # x0) ↔ (∀ b. b ∈ x0 → b = a) ⊦ a0 = a ∧ x0 = mklist(a, # x0) ↔ (∀ b. b = a0 ∨ b ∈ x0 → b = a)

Rule argument

spec: list inst: name: c-06 seq: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y subst: [y, b, x, a] → [mklist(a, # x0), a, x0, a0] flags: rewrite

Additional information

Used terms: mklist(a, # x0), a, x0, a0